ψ[x_,n_,t_]:=Exp[- x^2 /2]  HermiteH[n,x] Exp[- I (n +1/2)  t];

Manipulate[Plot[(ψ[x,1,t]+ψ[x,2,t]) Conjugate[ψ[x,1,t]+ψ[x,2,t]],{x,-4,4}],{t,0,13}]

coherent[x_,t_,a_]:=Exp[- a^2 /2]   Sum[(a^n  / (Sqrt[n!]))  ψ[x,n,t],{n,0,20}];

Plot[coherent[x,100,.01] Conjugate[coherent[x,100,.01]],{x,-4,4}]

Manipulate[Plot[coherent[x,t,a] Conjugate[coherent[x,t,a]],{x,-5,5}],{a,0.01,.99},{t,0,100}]